The Annals of Applied Probability

Social contact processes and the partner model

Eric Foxall, Roderick Edwards, and P. van den Driessche

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We consider a stochastic model of infection spread on the complete graph on $N$ vertices incorporating dynamic partnerships, which we assume to be monogamous. This can be seen as a variation on the contact process in which some form of edge dynamics determines the set of contacts at each moment in time. We identify a basic reproduction number $R_{0}$ with the property that if $R_{0}<1$ the infection dies out by time $O(\log N)$, while if $R_{0}>1$ the infection survives for an amount of time $e^{\gamma N}$ for some $\gamma>0$ and hovers around a uniquely determined metastable proportion of infectious individuals. The proof in both cases relies on comparison to a set of mean-field equations when the infection is widespread, and to a branching process when the infection is sparse.

Article information

Ann. Appl. Probab., Volume 26, Number 3 (2016), 1297-1328.

Received: December 2014
Revised: April 2015
First available in Project Euclid: 14 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 92B99: None of the above, but in this section

SIS model contact process interacting particle systems


Foxall, Eric; Edwards, Roderick; van den Driessche, P. Social contact processes and the partner model. Ann. Appl. Probab. 26 (2016), no. 3, 1297--1328. doi:10.1214/15-AAP1117.

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